Title
Asymptotic representation of solutions of nonlinear differential and difference equations with regularly varying coefficients: doctoral dissertation
Creator
Kapešić, Aleksandra B. 1988-
Copyright date
2020
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Select license
Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
License description
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Language
English
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 19.02.2021.
Other responsibilities
mentor
Manojlović, Jelena
član komisije
Đurčić, Dragan 1967-
član komisije
Jovanović, Miljana D. 1965-
član komisije
Kočinac, Ljubiša D. R. 1947-
Academic Expertise
Prirodno-matematičke nauke
Academic Title
-
University
Univerzitet u Nišu
Faculty
Prirodno-matematički fakultet
Group
Odsek za matematiku i informatiku
Alternative title
Asimptotska reprezentacija rešenja nelinearnih diferencijalnih i diferencnih jednačina sa pravilno promenljivim koeficijentima
Publisher
[A. B. Kapešić]
Format
VII, 156 str.
description
Bibliografija: str. 143-154;
Biografija sa bibliografijom: str. 155-156.
description
Differential and difference equations
Abstract (en)
In this dissertation, differential equations of the fourth order, difference
equation of second order and cyclic systems of difference equations of
second order are considered. In particular, assuming that coefficients of
fourth order differential equation of Emden-Fowler type are generalized
regularly varying functions, complete information about the existence of
all possible intermediate regularly varying solutions and their accurate
asymptotic behavior at infinity are given. The second order difference
equation of Thomas-Fermy type is discussed in the framework of discrete
regular variation and its strongly increasing and strongly decreasing
solutions are examined in detail. Necessary and sufficient conditions for
the existence of these solutions, as well as their asymptotic representations,
have been determined. The obtained results enabled the complete structure
of a set of regularly varying solutions to be presented. Cyclic systems of
difference equations are considered as a natural generalization of second
order difference equations. A full characterization of the limit behavior of
all positive solutions is established. In particular, the asymptotic behavior
of intermediate, as well as strongly increasing and strongly decreasing
solutions is analyzed under the assumption that coefficients of the systems
are regularly varying sequences and exact asymptotic formulas are derived
for all these types of solutions. Also, the conditions for the existence of all
types of positive solutions have been obtained.
Authors Key words
regularly varying functions, regularly varying sequences, asymptotic
behaviour of solutions, fourth order differential equation, nonlinear
difference equations, systems of difference equations
Authors Key words
pravilno promenljive funkcije, pravilno promenljivi nizovi,
asimptotsko ponašanje rešenja, diferencijalne jednačine četvrtog
reda, nelinearne diferencne jednačine, sistemi diferencnih
jednačina
Classification
517.928/.929(043.3)
Subject
P130
Type
Tekst
Abstract (en)
In this dissertation, differential equations of the fourth order, difference
equation of second order and cyclic systems of difference equations of
second order are considered. In particular, assuming that coefficients of
fourth order differential equation of Emden-Fowler type are generalized
regularly varying functions, complete information about the existence of
all possible intermediate regularly varying solutions and their accurate
asymptotic behavior at infinity are given. The second order difference
equation of Thomas-Fermy type is discussed in the framework of discrete
regular variation and its strongly increasing and strongly decreasing
solutions are examined in detail. Necessary and sufficient conditions for
the existence of these solutions, as well as their asymptotic representations,
have been determined. The obtained results enabled the complete structure
of a set of regularly varying solutions to be presented. Cyclic systems of
difference equations are considered as a natural generalization of second
order difference equations. A full characterization of the limit behavior of
all positive solutions is established. In particular, the asymptotic behavior
of intermediate, as well as strongly increasing and strongly decreasing
solutions is analyzed under the assumption that coefficients of the systems
are regularly varying sequences and exact asymptotic formulas are derived
for all these types of solutions. Also, the conditions for the existence of all
types of positive solutions have been obtained.
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